In order for the body swap to work, (f)Aegon would have to have been beaten into a unrecognizable state.
There are plenty of ways to brutal maim and kill people but very few would make them recognizable. For example Theon has gone through alot, but you could still barely physically recognize him.
I think in general into order to make somebody unrecongnizable you would have to use bludgeons to beat the body. Gregor uses a sword. Now accoding to Ned (?), Gregor apparently threw Aegon against a wall, but babies/people have fallen from large heights (which is comparable to being thrown against a Wall) and they were still recognizable.
Therefore either Gregor was in on the scheme, or Varys is lying.